With the help of contraction method we study the harmonic oscillator in spaces with degenerate metrics, namely, on Galilei plane and in the flat 3D Cayley-Klein spaces R 3 (j 2 , j 3). It is shown that the inner degrees of freedom are appeared which physical dimensions are different from the dimension of the space.

In this paper, we prove a global rigidity theorem for negatively curved Finsler metrics on a compact manifold of dimension n ≥ 3. We show that for such a Finsler manifold, if the flag curvature is a scalar function on the tangent bundle, then the Finsler metric is of Randers type. We also study the case when the Finsler metric is locally projectively flat.

We discuss general properties of the theory of higher spin gauge fields in AdS 4 focusing on the relationship between the star-product origin of the higher spin symmetries, AdS geometry and the concept of space-time locality. A full list of conserved higher spin currents in the flat space of arbitrary dimension is presented.

In this letter we present an idea which reconciles a homogeneous and isotropic Friedmann universe with a fractal distribution of galaxies. We use two observational facts: The flat rotation curves of galaxies and the (still debated) fractal distribution of galaxies with fractal dimension D = 2. Our idea can also be interpreted as a redefinition of the notion of bias.

A semi-dualizing module over a commutative noetherian ringA is a finitely generated module C with RHomA(C,C) ≃ A in the derived category D(A). We show how each such module gives rise to three new homological dimensions which we call C–Gorenstein projective, C–Gorenstein injective, and C–Gorenstein flat dimension, and investigate the properties of these dimensions.

This paper deals with the theortical investigation on curved FSS with wide band frequency. The FSS structure is designed by projecting some circular patches of same dimension on the dome shaped substrate. Compared to conventional Flat type FSS this design provide more wider band of frequency(7.09 GHz). Theoretical investigations have been done by CADFEKO(suite5.5) Designer® software.

We show that stationary, asymptotically flat solutions of the electrovacuum Einstein equations are analytic at i, for a large family of gauges, in odd space-time dimensions higher than seven. The same is true in space-time dimension five for static vacuum solutions with non-vanishing mass.

In the complex-Riemannian framework we show that a conformal manifold containing a compact, simply-connected, null-geodesic is conformally flat. In dimension 3 we use the LeBrun correspondence, that views a conformal 3-manifold as the conformal infinity of a selfdual four-manifolds. We also find a relation between the conformal invariants of the conformal infinity and its ambient.

Spectral Methods. The basic idea is to assume that the data lies on a manifold/surface in D-dimensional space, see figure (1) Perform multi-dimensional scaling, or other dimension reduction method, using distances calculated on the manifold, see figure (2). Figure 1. We assume that the data lies on a manifold. This is a surface which is locally flat.

We present a compact formula computing rational trigonometric sums. Such sums appeared in the work of E. Verlinde on the dimension of conformal blocks in WessZumino-Witten (WZW) theory. As an application, we show that a formula of J.-M. Bismut and F. Labourie for the Riemann-Roch numbers of moduli spaces of flat connections on a Riemann surface coincides with Verlinde’s expression.